The Journal of the Indian Mathematical Society

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Alternate Terms in Lucas Sequence


Affiliations
1 Centre for Advanced Study in Mathematics, Panjab University, Chandigarh-160014, India
2 Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Khanapara, Guwahati-781022, India
     

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In this paper we study the properties of L2n+1 which is the Lucas number of order 2n+1. Several properties like generating functions, recurrence relations, summation formulas and (q-analogues of L2n+1 were found by Agarwal in [1,2,3]. Here we obtain hypergeometric form, Integral representation and several congruence properties and identities for these numbers. Congruence properties are used to establish a theorem on periodicity of the sequence {L2n+1}n∞=0.
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  • Alternate Terms in Lucas Sequence

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Authors

A. K. Agarwal
Centre for Advanced Study in Mathematics, Panjab University, Chandigarh-160014, India
B. Dutta
Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Khanapara, Guwahati-781022, India

Abstract


In this paper we study the properties of L2n+1 which is the Lucas number of order 2n+1. Several properties like generating functions, recurrence relations, summation formulas and (q-analogues of L2n+1 were found by Agarwal in [1,2,3]. Here we obtain hypergeometric form, Integral representation and several congruence properties and identities for these numbers. Congruence properties are used to establish a theorem on periodicity of the sequence {L2n+1}n∞=0.